Finite Group Databasebeta

← #30616876

Subgroups — #30616876

Order 15616.

1560 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840829C211yesmaximal, characteristic
2C2×#16840801C211yesmaximal, characteristic, complemented
3C2×SD16×#6923C211yesmaximal, characteristic, complemented
4#21462306C211yesmaximal, characteristic, complemented
5#21461812C211yesmaximal, characteristic, complemented
6#21461812C211yesmaximal, characteristic, complemented
7#21461805C211yesmaximal, characteristic, complemented
8#21461784C211yesmaximal, characteristic, complemented
9#21461782C211yesmaximal, characteristic, complemented
10#21461770C211yesmaximal, characteristic, complemented
11#21461657C211yesmaximal, characteristic
12#21461590C211yesmaximal, characteristic, complemented
13#102×#6923C211yesmaximal, characteristic, complemented
14#21461550C211yesmaximal, characteristic, complemented
15#450×D61C211yesmaximal, characteristic
16#16840829—24no—
17#16840829—24no—
18C2×Q8×#6923C2211yescharacteristic, complemented
19C2×D4×#6923—21no—
20C2×D4×#6923—21no—
21C2×D4×#6923C2211yescharacteristic
22C2×D4×#6923C2211yescharacteristic
23C2×D4×#6923C2211yescharacteristic
24C2×D4×#6923C2211yescharacteristic
25C2×#14519856C2211yescharacteristic
26C2×#14519856C2211yescharacteristic
27C22×C22⋊#6923—21no—
28C22×C22⋊#6923—21no—
29#16840801—24no—
30SD16×#6923—24no—
31C2×#14519846C2211yescharacteristic, complemented
32C2×#14519845C2211yescharacteristic, complemented
33C2×#14519840C2211yescharacteristic, complemented
34C2×#14519840C2211yescharacteristic, complemented
35C2×#14519839C2211yescharacteristic
36C2×#14519839C2211yescharacteristic
37C2×#14519839C2211yescharacteristic
38C2×#14519839C2211yescharacteristic
39D61⋊(C22⋊C8)C2211yescharacteristic
40C2×#14519831C2211yescharacteristic, complemented
41C2×C8×#6923C2211yescharacteristic, complemented
42(C2×#6923)⋊Q8C2211yescharacteristic, complemented
43#16840713—21no—
44#16840713C2211yescharacteristic, complemented
45#16840712—21no—
46#16840712—21no—
47#16840711—21no—
48#16840704C2211yescharacteristic
49C4⋊C4×#6923C2211yescharacteristic, complemented
50#16840636C2211yescharacteristic, complemented
51#16840636C2211yescharacteristic, complemented
52#16840635C2211yescharacteristic, complemented
53#16840635C2211yescharacteristic, complemented
54(C2×#6923)⋊C8C2211yescharacteristic, complemented
55(C2×#6923)⋊C8C2211yescharacteristic, complemented
56C22×D4×D61C2211yescharacteristic
57C2×SD16×D61C2211yescharacteristic
58C2×SD16×D61C2211yescharacteristic
59C22⋊Q8×D61C2211yescharacteristic
60#16839915C411yescharacteristic, complemented
61#16839914C411yescharacteristic, complemented
62#16839914C411yescharacteristic, complemented
63#16839913C411yescharacteristic, complemented
64#16839912C411yescharacteristic, complemented
65#16839911C411yescharacteristic, complemented
66#16839911C411yescharacteristic, complemented
67#102×D61C2211yescharacteristic
68#102×D61C2211yescharacteristic
69C22⋊C8×D61C2211yescharacteristic
70C61×#450C411yescharacteristic, complemented
71C23×#6923—21no—
72C23×#6923—21no—
73C23×#6923—21no—
74C23×#6923—21no—
75C2×D61⋊C8C2311yescharacteristic
76C2×D61⋊C8C2311yescharacteristic
77Q8×#6923—22no—
78Q8×#6923—22no—
79D4×#6923—28no—
80D4×#6923—28no—
81D4×#6923—22no—
82D4×#6923—22no—
83D4×#6923—22no—
84D4×#6923—22no—
85D4×#6923—22no—
86D4×#6923—22no—
87D4×#6923D414yes—
88D4×#6923D414yes—
89#14519856—22no—
90#14519856—22no—
91#14519856—22no—
92#14519856—22no—
93C2×C4⋊#6923—21no—
94C2×C4⋊#6923—21no—
95C2×C4⋊#6923D411yescharacteristic
96C2×C4⋊#6923D411yescharacteristic
97C2×C4⋊#6923C2311yescharacteristic
98C2×C4⋊#6923C2311yescharacteristic
99C2×C4⋊#6923C2311yescharacteristic
100C2×C4⋊#6923C2311yescharacteristic
101C2×C22⋊#6923—28no—
102C2×C22⋊#6923—28no—
103C2×C22⋊#6923—21no—
104C2×C22⋊#6923—21no—
105C2×C22⋊#6923—21no—
106C2×C22⋊#6923—21no—
107C2×C22⋊#6923—21no—
108C2×C22⋊#6923—21no—
109C2×C22⋊#6923D411yescharacteristic
110C2×C22⋊#6923D411yescharacteristic
111C2×C4×#6923—21no—
112C2×C4×#6923—21no—
113C2×C4×#6923—21no—
114C2×C4×#6923C2311yescharacteristic
115C2×C4×#6923C2311yescharacteristic
116#14519846—22no—
117#14519845—22no—
118#14519840—22no—
119#14519840—22no—
120#14519839—22no—
121#14519839—22no—
122#14519839—22no—
123#14519839—22no—
124#14519834—21no—
125C22⋊#92420—21no—
126#14519831—22no—
127C8×#6923—22no—
128(C2×#6923)⋊C4—21no—
129(C2×#6923)⋊C4—21no—
130(C2×#6923)⋊C4—21no—
131(C2×#6923)⋊C4—21no—
132(C2×#6923)⋊C4—21no—
133C24×D61—21no—
134C2×Q8×D61C2311yescharacteristic
135C22×D244C2×C411yescharacteristic
136C22×C22⋊D61—21no—
137C2×D4×D61—22no—
138C2×D4×D61—22no—
139C2×D4×D61—22no—
140C2×D4×D61—22no—
141C2×D4×D61—21no—
142C2×D4×D61—21no—
143C2×D4×D61C2×C411yescharacteristic
144C2×D4×D61C2×C411yescharacteristic
145C2×D4×D61C2311yescharacteristic
146C2×D4×D61C2311yescharacteristic
147C22×C4×D61C2311yescharacteristic
148C2×#11758190C2×C411yescharacteristic, complemented
149C2×#11758190C2×C411yescharacteristic, complemented
150C2×#11758200C2×C411yescharacteristic, complemented
151C2×#11758200C2×C411yescharacteristic, complemented
152C2×#11758201C2×C411yescharacteristic, complemented
153C2×#11758201C2×C411yescharacteristic, complemented
154SD16×D61—22no—
155SD16×D61—22no—
156SD16×D61—22no—
157SD16×D61—22no—
158C2×C8×D61C2311yescharacteristic
159C2×C8×D61C2311yescharacteristic
160#14519757C2×C411yescharacteristic, complemented
161#14519756C2×C411yescharacteristic, complemented
162#14519755—21no—
163#14519754—21no—
164#14519753C2×C411yescharacteristic, complemented
165C4⋊C4×D61—21no—
166C4⋊C4×D61C2311yescharacteristic
167C22⋊C4×D61—21no—
168#14519699C2×C411yescharacteristic, complemented
169#14519699C2×C411yescharacteristic, complemented
170#14519698C2×C411yescharacteristic, complemented
171#14519698C2×C411yescharacteristic, complemented
172#14519697C2×C411yescharacteristic, complemented
173#14519697C2×C411yescharacteristic, complemented
174C22⋊#92418C2×C411yescharacteristic, complemented
175#14519689C2×C411yescharacteristic, complemented
176#14519689C2×C411yescharacteristic, complemented
177C22×D4×C61C2×C411yescharacteristic
178C2×SD16×C61C2×C411yescharacteristic, complemented
179C2×SD16×C61C2×C411yescharacteristic, complemented
180C22⋊Q8×C61C2×C411yescharacteristic, complemented
181#102×C61C2×C411yescharacteristic, complemented
182#102×C61C2×C411yescharacteristic, complemented
183C22⋊C8×C61C2×C411yescharacteristic, complemented
184C24×C61—21no—
185C23×D61—24no—
186C23×D61—24no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—81no—
193C23×D61—81no—
194C23×D61—81no—
195C23×D61—81no—
196C23×D61C2×D411yescharacteristic
197C22×#6923—21no—
198C22×#6923—21no—
199C22×#6923—24no—
200C22×#6923—24no—
201C22×#6923—24no—
202C22×#6923—24no—
203C22×#6923—21no—
204C22×#6923—21no—
205C22×#6923—81no—
206C22×#6923—81no—
207C22×#6923—81no—
208C22×#6923—81no—
209C22×#6923—81no—
210C22×#6923—81no—
211C22×#6923—81no—
212C22×#6923—81no—
213C22×#6923C2×D411yescharacteristic
214C22×#6923C2×D411yescharacteristic
215C22×#6923C2×D411yescharacteristic
216C22×#6923C2×D411yescharacteristic
217C2×Q8×C61C22×C411yescharacteristic
218C2×D4×C61—22no—
219C2×D4×C61—22no—
220C2×D4×C61—21no—
221C2×D4×C61C22×C411yescharacteristic
222C2×D4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C2×C22⋊D61—24no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C22×Dic61#4111yescharacteristic
231Q8×D61—21no—
232Q8×D61—21no—
233Q8×D61—21no—
234Q8×D61—21no—
235D4×D61—24no—
236D4×D61—24no—
237D4×D61—24no—
238D4×D61—24no—
239D4×D61—22no—
240D4×D61—22no—
241D4×D61—22no—
242D4×D61—22no—
243D4×D61—21no—
244D4×D61—21no—
245D4×D61—21no—
246D4×D61—21no—
247D4×D61C2×D412yes—
248D4×D61C2×D412yes—
249D4×D61#4112yes—
250D4×D61#4112yes—
251C2×D244—21no—
252C2×D244—22no—
253C2×D244—22no—
254C2×D244C22×C411yescharacteristic
255C2×D244C22×C411yescharacteristic
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61C22×C411yescharacteristic
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61#4111yescharacteristic
265C2×C4×D61C2411yescharacteristic
266C2×Dic122—21no—
267C2×Dic122C22×C411yescharacteristic
268C22⋊#6923—24no—
269C22⋊#6923—24no—
270C22⋊#6923—24no—
271C22⋊#6923—22no—
272C22⋊#6923—22no—
273C22⋊#6923—24no—
274C22⋊#6923—24no—
275C22⋊#6923—81no—
276C2×#92420—21no—
277C2×#92420—21no—
278C4⋊#6923—22no—
279C4⋊#6923—22no—
280C4⋊#6923—21no—
281C4⋊#6923—21no—
282C4⋊#6923—21no—
283C4⋊#6923—21no—
284C4⋊#6923—21no—
285C4⋊#6923—21no—
286C4⋊#6923—42no—
287C4⋊#6923—81no—
288C4⋊#6923C2×D412yes—
289C4⋊#6923C2×D412yes—
290C4×#6923—24no—
291C4×#6923—21no—
292C4×#6923—21no—
293C4×#6923—42no—
294C4×#6923—81no—
295C4×#6923C2×D412yes—
296C4×#6923C2×D412yes—
297D61⋊C8—21no—
298D61⋊C8—21no—
299D61⋊C8—21no—
300D61⋊C8—21no—
301SD16×C61—22no—
302SD16×C61—22no—
303C2×C8×C61C22×C411yescharacteristic
304C2×C8×C61C22×C411yescharacteristic
305C4⋊C4×C61—21no—
306C4⋊C4×C61C22×C411yescharacteristic
307C22⋊C4×C61—21no—
308C22⋊Dic61—21no—
309#11758201—22no—
310#11758201—22no—
311#11758200—22no—
312#11758200—22no—
313#11758198—21no—
314#11758198—21no—
315C4⋊Dic61—21no—
316C4⋊Dic61C22×C411yescharacteristic
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320C2×#92418C22×C411yescharacteristic
321C2×#92418C22×C411yescharacteristic
322#11758190—22no—
323#11758190—22no—
324C8×D61—21no—
325C8×D61—21no—
326C8×D61—21no—
327C8×D61—21no—
328C23×C61—24no—
329C23×C61—21no—
330C23×C61—21no—
331C23×C61—81no—
332C23×C61—81no—
333C23×C61C4×D411yescharacteristic
334C22×D61—21no—
335C22×D61—21no—
336C22×D61—24no—
337C22×D61—24no—
338C22×D61—24no—
339C22×D61—21no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—21no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—81no—
358C22×D61—81no—
359C22×D61—81no—
360C22×D61—81no—
361C22×D61—84no—
362C22×D61—84no—
363C22×D61—84no—
364C22×D61—84no—
365C22×D61—81no—
366C22×D61—81no—
367C22×D61C4×D411yescharacteristic
368C22×D61C22×D411yescharacteristic
369C2×#6923—21no—
370C2×#6923—21no—
371C2×#6923—21no—
372C2×#6923—21no—
373C2×#6923—21no—
374C2×#6923—21no—
375C2×#6923—22no—
376C2×#6923—22no—
377C2×#6923—21no—
378C2×#6923—21no—
379C2×#6923—21no—
380C2×#6923—21no—
381C2×#6923—41no—
382C2×#6923—41no—
383C2×#6923—41no—
384C2×#6923—41no—
385C2×#6923—41no—
386C2×#6923—41no—
387C2×#6923—41no—
388C2×#6923—41no—
389C2×#6923—41no—
390C2×#6923—41no—
391C2×#6923—84no—
392C2×#6923—84no—
393C2×#6923—84no—
394C2×#6923—84no—
395C2×#6923#12012yes—
396C2×#6923#12012yes—
397Q8×C61—21no—
398Q8×C61—21no—
399D4×C61—24no—
400D4×C61—21no—
401D4×C61—21no—
402D4×C61C4×D412yes—
403D4×C61C4×D412yes—
404C2×C4×C61—21no—
405C2×C4×C61—21no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61C4×D411yescharacteristic
409C2×C4×C61C23×C411yescharacteristic
410C22⋊D61—24no—
411C22⋊D61—24no—
412C22⋊D61—22no—
413C22⋊D61—22no—
414C22⋊D61—22no—
415C22⋊D61—22no—
416C2×Dic61—21no—
417C2×Dic61—21no—
418C2×Dic61—21no—
419C2×Dic61—21no—
420C2×Dic61C4×D411yescharacteristic
421C2×Dic61C2×#4111yescharacteristic
422D244—24no—
423D244—21no—
424D244—21no—
425D244C4×D412yes—
426D244C4×D412yes—
427C4×D61—21no—
428C4×D61—21no—
429C4×D61—21no—
430C4×D61—21no—
431C4×D61—21no—
432C4×D61—21no—
433C4×D61—41no—
434C4×D61—41no—
435C4×D61—41no—
436C4×D61—41no—
437C4×D61C22×D411yescharacteristic
438C4×D61C22×D411yescharacteristic
439C4×D61C2×#4111yescharacteristic
440C4×D61C2×#4111yescharacteristic
441Dic122—21no—
442Dic122—21no—
443Dic122—41no—
444Dic122—41no—
445#92420—41no—
446#92420—41no—
447C8×C61—21no—
448C8×C61—21no—
449#92418—21no—
450#92418—21no—
451#21459—611nomaximal, Sylow
452C22×C61—21no—
453C22×C61—21no—
454C22×C61—21no—
455C22×C61—22no—
456C22×C61—22no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61—41no—
460C22×C61—41no—
461C22×C61—84no—
462C22×C61C2×C4×D411yescharacteristic
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—21no—
466C2×D61—22no—
467C2×D61—22no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—41no—
471C2×D61—41no—
472C2×D61—41no—
473C2×D61—42no—
474C2×D61—42no—
475C2×D61—41no—
476C2×D61—42no—
477C2×D61—42no—
478C2×D61—42no—
479C2×D61—42no—
480C2×D61—41no—
481C2×D61—42no—
482C2×D61—42no—
483C2×D61—41no—
484C2×D61—84no—
485C2×D61—84no—
486C2×D61—84no—
487C2×D61C2×#12011yescharacteristic
488C2×D61#52511yescharacteristic
489C2×D61#57611yescharacteristic
490C2×D61#57711yescharacteristic
491C2×D61#57711yescharacteristic
492C2×D61#57711yescharacteristic
493#6923—22no—
494#6923—22no—
495#6923—41no—
496#6923—42no—
497#6923—41no—
498#6923—42no—
499#6923—81no—
500#6923—81no—
501C4×C61—21no—
502C4×C61—41no—
503C4×C61—41no—
504C4×C61C2×C4×D411yescharacteristic
505C4×C61C2×C4×D411yescharacteristic
506Dic61—21no—
507Dic61—41no—
508Dic61—41no—
509Dic61#52511yescharacteristic
510Dic61#52511yescharacteristic
511C2×#518—611no—
512C2×#450—611no—
513C2×#440—611no—
514C2×C4×SD16—611no—
515#2323—611no—
516#1877—611no—
517#1877—611no—
518#1873—611no—
519#1864—611no—
520#1862—611no—
521#1854—611no—
522#1786—611no—
523#1762—611no—
524C4×#102—611no—
525#1750—611no—
526C2×C61—41no—
527C2×C61—42no—
528C2×C61—42no—
529C2×C61C4×#12011yescharacteristic
530C2×C61#294611yescharacteristic
531C2×C61#294911yescharacteristic
532D61—41no—
533D61—42no—
534D61—42no—
535D61#300911yescharacteristic
536D61#301211yescharacteristic
537D61#311811yescharacteristic
538D61#312311yescharacteristic
539C23×D4—611no—
540C22×SD16—611no—
541C22×SD16—611no—
542C2×C22⋊Q8—611no—
543#518—1224no—
544#518—1224no—
545C2×C4×Q8—611no—
546C2×C4×D4—611no—
547C2×C4×D4—611no—
548C2×C4×D4—611no—
549C2×C4×D4—611no—
550C2×C4×D4—1221no—
551C2×C4×D4—1221no—
552C2×#117—611no—
553C2×#117—611no—
554C22×C22⋊C4—1221no—
555C22×C22⋊C4—1221no—
556#450—611no—
557#450—611no—
558#450—611no—
559#450—611no—
560#450—611no—
561#450—611no—
562#450—611no—
563#450#692311yescharacteristic, complemented
564#440—1224no—
565C4×SD16—1224no—
566C2×#107—611no—
567C2×#106—611no—
568C2×#103—611no—
569C2×#103—611no—
570C2×#102—611no—
571C2×#102—611no—
572C2×#102—611no—
573C2×#102—611no—
574C2×#102—611no—
575C2×#102—611no—
576C2×C22⋊C8—611no—
577C2×C22⋊C8—611no—
578C2×#97—611no—
579C2×C4×C8—611no—
580#391—611no—
581#389—611no—
582#389—1221no—
583#388—1221no—
584#388—1221no—
585#387—1221no—
586#380—611no—
587C4×C4⋊C4—611no—
588#340—611no—
589#340—611no—
590#340—611no—
591#340—611no—
592#336—611no—
593#336—611no—
594C61#2145911yescharacteristic, complemented, Sylow
595C25—1221no—
596C22×Q8—611no—
597C22×D4—611no—
598C22×D4—611no—
599C22×D4—611no—
600C22×D4—611no—
601C22×D4—611no—
602C22×D4—1221no—
603C22×D4—1221no—
604C22×D4—1221no—
605C22×D4—1222no—
606C22×D4—1222no—
607C22×D4—1222no—
608C22×D4—1222no—
609C22×D4C2×#692311yescharacteristic
610C23×C4—611no—
611C23×C4—1221no—
612C23×C4—1221no—
613C23×C4—1221no—
614C23×C4—1221no—
615C2×SD16—611no—
616C2×SD16—611no—
617C2×SD16—611no—
618C2×SD16—611no—
619C2×SD16—611no—
620C2×SD16—611no—
621C2×SD16—1222no—
622C2×SD16—1222no—
623C2×SD16—1222no—
624C2×SD16—1222no—
625C2×SD16C2×#692311yescharacteristic, complemented
626C2×SD16C2×#692311yescharacteristic, complemented
627C22×C8—611no—
628C22×C8—611no—
629C22×C8—611no—
630C22×C8—611no—
631C22⋊Q8—611no—
632C22⋊Q8—611no—
633C22⋊Q8—611no—
634C22⋊Q8—1221no—
635C22⋊Q8—1221no—
636C22⋊Q8C2×#692311yescharacteristic, complemented
637C4×Q8—1222no—
638C4×Q8—1222no—
639C4×D4—614no—
640C4×D4—614no—
641C4×D4—1222no—
642C4×D4—1222no—
643C4×D4—1222no—
644C4×D4—1222no—
645C4×D4—1222no—
646C4×D4—1222no—
647C4×D4—1228no—
648C4×D4—1228no—
649#117—1222no—
650#117—1222no—
651#117—1222no—
652#117—1222no—
653C2×C4⋊C4—611no—
654C2×C4⋊C4—611no—
655C2×C4⋊C4—611no—
656C2×C4⋊C4—611no—
657C2×C4⋊C4—611no—
658C2×C4⋊C4—611no—
659C2×C4⋊C4—611no—
660C2×C4⋊C4—1221no—
661C2×C4⋊C4—1221no—
662C2×C4⋊C4—1221no—
663C2×C22⋊C4—611no—
664C2×C22⋊C4—611no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C22⋊C4—1221no—
670C2×C22⋊C4—1221no—
671C2×C22⋊C4—1228no—
672C2×C22⋊C4—1228no—
673C2×C22⋊C4—1221no—
674C2×C42—611no—
675C2×C42—611no—
676C2×C42—1221no—
677C2×C42—1221no—
678C2×C42—1221no—
679#107—1222no—
680#106—1222no—
681#103—1222no—
682#103—1222no—
683#102—611no—
684#102—611no—
685#102—611no—
686#102—611no—
687#102—611no—
688#102—611no—
689#102—1222no—
690#102—1222no—
691#102—1222no—
692#102—1222no—
693#102C2×#692311yescharacteristic, complemented
694#102C2×#692311yescharacteristic, complemented
695C22⋊C8—611no—
696C22⋊C8—611no—
697C22⋊C8—611no—
698C22⋊C8—1221no—
699C22⋊C8—1221no—
700C22⋊C8C2×#692311yescharacteristic, complemented
701#97—1222no—
702C4×C8—1222no—
703#95—1221no—
704#95—1221no—
705#95—1221no—
706#95—1221no—
707#95—1221no—
708C24—21no—
709C24—611no—
710C24—1221no—
711C24—1221no—
712C24—1221no—
713C24—1221no—
714C24—1224no—
715C24—1224no—
716C24—1221no—
717C24—4881no—
718C24—4881no—
719C24—4881no—
720C24—4881no—
721C2×Q8—611no—
722C2×Q8—1221no—
723C2×Q8—1221no—
724C2×Q8—1221no—
725C2×Q8—1221no—
726C2×Q8—1221no—
727C2×Q8C22×#692311yescharacteristic
728C2×D4—22no—
729C2×D4—22no—
730C2×D4—21no—
731C2×D4—612no—
732C2×D4—612no—
733C2×D4—612no—
734C2×D4—612no—
735C2×D4—611no—
736C2×D4—611no—
737C2×D4—1222no—
738C2×D4—1222no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—1221no—
744C2×D4—1221no—
745C2×D4—1221no—
746C2×D4—1221no—
747C2×D4—1222no—
748C2×D4—1222no—
749C2×D4—1224no—
750C2×D4—1224no—
751C2×D4—1224no—
752C2×D4—1224no—
753C2×D4—1224no—
754C2×D4—1224no—
755C2×D4—1222no—
756C2×D4—1222no—
757C2×D4—1221no—
758C2×D4C22×#692311yescharacteristic
759C2×D4C22×#692311yescharacteristic
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—611no—
765C22×C4—611no—
766C22×C4—611no—
767C22×C4—611no—
768C22×C4—611no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1224no—
776C22×C4—1224no—
777C22×C4—1224no—
778C22×C4—1224no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—4881no—
784C22×C4—4881no—
785C22×C4—4881no—
786C22×C4—4881no—
787C22×C4—4881no—
788C22×C4—4881no—
789C22×C4—4881no—
790C22×C4—4881no—
791C22×C4C22×#692311yescharacteristic
792SD16—22no—
793SD16—22no—
794SD16—1222no—
795SD16—1222no—
796SD16—1222no—
797SD16—1222no—
798SD16—1222no—
799SD16—1222no—
800C2×C8—611no—
801C2×C8—611no—
802C2×C8—1221no—
803C2×C8—1221no—
804C2×C8—1221no—
805C2×C8—1221no—
806C2×C8—1221no—
807C2×C8—1221no—
808C2×C8—1221no—
809C2×C8—1221no—
810C2×C8—1221no—
811C2×C8—1221no—
812C2×C8C22×#692311yescharacteristic
813C2×C8C22×#692311yescharacteristic
814C4⋊C4—21no—
815C4⋊C4—612no—
816C4⋊C4—612no—
817C4⋊C4—611no—
818C4⋊C4—1221no—
819C4⋊C4—1221no—
820C4⋊C4—1221no—
821C4⋊C4—1221no—
822C4⋊C4—1221no—
823C4⋊C4—1222no—
824C4⋊C4—1222no—
825C4⋊C4—1221no—
826C4⋊C4—1221no—
827C4⋊C4—1221no—
828C4⋊C4—1221no—
829C4⋊C4—1221no—
830C4⋊C4—4881no—
831C4⋊C4—2442no—
832C4⋊C4C22×#692311yescharacteristic
833C22⋊C4—21no—
834C22⋊C4—1221no—
835C22⋊C4—1221no—
836C22⋊C4—1222no—
837C22⋊C4—1222no—
838C22⋊C4—1224no—
839C22⋊C4—1224no—
840C22⋊C4—1224no—
841C22⋊C4—1224no—
842C22⋊C4—1224no—
843C22⋊C4—1221no—
844C22⋊C4—4881no—
845C42—612no—
846C42—612no—
847C42—1221no—
848C42—1221no—
849C42—1224no—
850C42—4881no—
851C42—2442no—
852C23—24no—
853C23—21no—
854C23—21no—
855C23—81no—
856C23—81no—
857C23—611no—
858C23—611no—
859C23—1221no—
860C23—1222no—
861C23—1222no—
862C23—1221no—
863C23—1221no—
864C23—1222no—
865C23—1222no—
866C23—1221no—
867C23—1221no—
868C23—1221no—
869C23—1224no—
870C23—1224no—
871C23—1224no—
872C23—1221no—
873C23—1221no—
874C23—4881no—
875C23—4881no—
876C23—4881no—
877C23—4881no—
878C23—4881no—
879C23—4881no—
880C23—4884no—
881C23—4884no—
882C23—4884no—
883C23—4884no—
884C23—2441no—
885C23—2441no—
886C23—2441no—
887C23—2441no—
888C23—2441no—
889C23—2441no—
890C23—2441no—
891C23—2441no—
892C23D4×#692311yescharacteristic
893Q8—21no—
894Q8—21no—
895Q8—1221no—
896Q8—1221no—
897Q8—2441no—
898Q8—2441no—
899D4—24no—
900D4—21no—
901D4—21no—
902D4—612no—
903D4—612no—
904D4—1224no—
905D4—1222no—
906D4—1222no—
907D4—1222no—
908D4—1222no—
909D4—1224no—
910D4—1224no—
911D4—1221no—
912D4—1221no—
913D4D4×#692312yes—
914D4D4×#692312yes—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—611no—
920C2×C4—611no—
921C2×C4—611no—
922C2×C4—611no—
923C2×C4—611no—
924C2×C4—612no—
925C2×C4—612no—
926C2×C4—611no—
927C2×C4—1221no—
928C2×C4—1221no—
929C2×C4—1221no—
930C2×C4—1221no—
931C2×C4—1221no—
932C2×C4—1221no—
933C2×C4—1221no—
934C2×C4—1221no—
935C2×C4—1221no—
936C2×C4—1221no—
937C2×C4—1221no—
938C2×C4—1221no—
939C2×C4—1222no—
940C2×C4—1222no—
941C2×C4—1221no—
942C2×C4—1221no—
943C2×C4—1221no—
944C2×C4—1221no—
945C2×C4—1221no—
946C2×C4—1221no—
947C2×C4—1221no—
948C2×C4—1221no—
949C2×C4—4884no—
950C2×C4—4884no—
951C2×C4—4884no—
952C2×C4—4884no—
953C2×C4—2441no—
954C2×C4—2441no—
955C2×C4—2441no—
956C2×C4—2441no—
957C2×C4—2441no—
958C2×C4—2441no—
959C2×C4—2441no—
960C2×C4—2441no—
961C2×C4—2441no—
962C2×C4—2441no—
963C2×C4—2441no—
964C2×C4—2441no—
965C2×C4—2441no—
966C2×C4—2441no—
967C2×C4D4×#692311yescharacteristic
968C2×C4C23×#692311yescharacteristic
969C8—21no—
970C8—21no—
971C8—1221no—
972C8—1221no—
973C8—2441no—
974C8—2441no—
975C22—21no—
976C22—22no—
977C22—22no—
978C22—21no—
979C22—21no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—41no—
984C22—84no—
985C22—611no—
986C22—611no—
987C22—611no—
988C22—611no—
989C22—611no—
990C22—611no—
991C22—1221no—
992C22—1222no—
993C22—1222no—
994C22—1221no—
995C22—1221no—
996C22—4884no—
997C22—4884no—
998C22—4884no—
999C22—2442no—
1000C22—2442no—
1001C22—2442no—
1002C22—2442no—
1003C22—2441no—
1004C22—2441no—
1005C22—2441no—
1006C22—2441no—
1007C22—2442no—
1008C22—2442no—
1009C22—2442no—
1010C22—2442no—
1011C22—2441no—
1012C22—2441no—
1013C22—2441no—
1014C22—2441no—
1015C22C2×D4×#692311yescharacteristic
1016C4—21no—
1017C4—41no—
1018C4—41no—
1019C4—611no—
1020C4—611no—
1021C4—1222no—
1022C4—1222no—
1023C4—1221no—
1024C4—4881no—
1025C4—4881no—
1026C4—2441no—
1027C4—2441no—
1028C4—2442no—
1029C4—2442no—
1030C4—2441no—
1031C4—2441no—
1032C4C2×D4×#692311yescharacteristic
1033C4C2×D4×#692311yescharacteristic
1034C2—41no—
1035C2—42no—
1036C2—42no—
1037C2—611no—
1038C2—611no—
1039C2—611no—
1040C2—611no—
1041C2—2441no—
1042C2—2442no—
1043C2—2442no—
1044C2#120×#692311yescharacteristic
1045C2#2146257611yescharacteristic
1046C2#2146257911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#450C4
socleC22×C61C2×C4×D4
prime radicalC22×D4×D61C22
cosocleC2×C4×D61C24
hypercenter#450#6923
hypocenterC61#21459
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16840801C2semidirect
3. C2×SD16×#6923C2semidirect
4. #21462306C2semidirect
5. #21461812C2semidirect
6. #21461812C2semidirect
7. #21461805C2semidirect
8. #21461784C2semidirect
9. #21461782C2semidirect
10. #21461770C2semidirect
12. #21461590C2semidirect
13. #102×#6923C2semidirect
14. #21461550C2semidirect
18. C2×Q8×#6923C22semidirect
31. C2×#14519846C22semidirect
32. C2×#14519845C22semidirect
33. C2×#14519840C22semidirect
34. C2×#14519840C22semidirect
40. C2×#14519831C22semidirect
41. C2×C8×#6923C22semidirect
42. (C2×#6923)⋊Q8C22semidirect
44. #16840713C22semidirect
49. C4⋊C4×#6923C22semidirect
50. #16840636C22semidirect
51. #16840636C22semidirect
52. #16840635C22semidirect
53. #16840635C22semidirect
54. (C2×#6923)⋊C8C22semidirect
55. (C2×#6923)⋊C8C22semidirect
60. #16839915C4semidirect
61. #16839914C4semidirect
62. #16839914C4semidirect
63. #16839913C4semidirect
64. #16839912C4semidirect
65. #16839911C4semidirect
66. #16839911C4semidirect
70. C61×#450C4semidirect
148. C2×#11758190C2×C4semidirect
149. C2×#11758190C2×C4semidirect
150. C2×#11758200C2×C4semidirect
151. C2×#11758200C2×C4semidirect
152. C2×#11758201C2×C4semidirect
153. C2×#11758201C2×C4semidirect
160. #14519757C2×C4semidirect
161. #14519756C2×C4semidirect
164. #14519753C2×C4semidirect
168. #14519699C2×C4semidirect
169. #14519699C2×C4semidirect
170. #14519698C2×C4semidirect
171. #14519698C2×C4semidirect
172. #14519697C2×C4semidirect
173. #14519697C2×C4semidirect
174. C22⋊#92418C2×C4semidirect
175. #14519689C2×C4semidirect
176. #14519689C2×C4semidirect
178. C2×SD16×C61C2×C4semidirect
179. C2×SD16×C61C2×C4semidirect
180. C22⋊Q8×C61C2×C4semidirect
181. #102×C61C2×C4semidirect
182. #102×C61C2×C4semidirect
183. C22⋊C8×C61C2×C4semidirect
563. #450#6923semidirect
594. C61#21459semidirect
625. C2×SD16C2×#6923semidirect
626. C2×SD16C2×#6923semidirect
636. C22⋊Q8C2×#6923semidirect
693. #102C2×#6923semidirect
694. #102C2×#6923semidirect
700. C22⋊C8C2×#6923semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168408292
C2×#168408012
C2×SD16×#69232
#214623062
#214618122
#214618052
#214617842
#214617822
#214617702
#214616572
#214615902
#102×#69232
#214615502
#450×D612
#2145961